The Sommerfeld Halfspace Problem Redux: Alternative Field Representations, Role of Zenneck and Surface Plasmon Waves

The problem of a vertical Hertzian dipole radiating in the presence of a lossy conducting halfspace, first formally solved by Sommerfeld in 1909, is revisited. Using rigorous operator theory concepts and the characteristic Green function procedure, alternative field representations are developed and their merits discussed. A closed-form asymptotic expression for the surface field is also derived and the role of the Zenneck and surface plasmon (SP) waves is elucidated. Numerical results are presented to validate the theory, including examples from radio to THz frequencies.